Constrained colliders in entanglement swapping

[Sambuco]

I'm opening this thread to discuss entanglement swapping in the context of constrained colliders (the Price-Wharton proposal) and their relationship to retrocausality, and so that Ken Wharton himself can clarify some issues.

Lucas.

 

[Ken Wharton]

Thanks, Lucas! I'm new to Physics Forums, so apologies in advance if I'm not clear on some of the norms here. I'm a physics professor at San Jose State U., working in quantum foundations since it became safe to do so -- in other words, since I got tenure in 2006. :-)

This paper is probably the most relevant to what you were discussing in that other thread, concerning the potential relationship between entanglement swapping and constrained colliders: https://arxiv.org/pdf/2406.04571 . There's a much more recent one, just posted, but that's pushing in a different direction.

In the context of entanglement swapping, the central measurement is trivially a "collider" in the causal modeling sense (multiple incoming causes contribute to a single effect). That's not retrocausal. But if the collider is in turn *constrained* -- say, a future boundary constraint on what is allowed to happen -- then what happens on one side of the experiment can be said to influence what happens on the other, via a zig-zag link that is in part retrocausal. (The motivation is that by allowing some hidden retrocausality, one can recover a local-mediation along the worldlines in any entanglement experiment, without faster-than-light or directly-nonlocal influences, as described here: https://arxiv.org/abs/1906.04313 )

I'm more than happy to answer any related questions.

 

[Sambuco]

Thanks Ken for joining us!

I would like to ask you about your perspective on the relationship between the concept of constrained colliders and the interpretation of quantum mechanics.

I see constrained colliders as a useful concept within information-based interpretations, such as relational quantum mechanics, where the "real stuff" consists of events distributed throughout space-time and causation is not fundamental, more in line with an all-at-once interpretation, such as that advocated by Emily Adlam in recent papers.

On the other hand, in the conclusions of the article you shared, it is explicitly stated:
"We have argued that in both V-shaped and W-shaped cases, Bell nonlocality can result from a combination of two things: (i) causal influences operating within the lightcones; and (ii) boundary constraints, restricting the possible values of collider variables."
I find the concept of a "real" retrocausality more in line with a $\Psi$-ontic interpretation, that is, it is on the opposite side of the interpretations I mentioned earlier. Is retrocausality considered as something "real" in your papers? Do you think your work fit more into one of the usual interpretations?

Lucas.

 

[Ken Wharton]

Hi Lucas,

Thanks for the question! I’d like to understand your perspective better, in part because it’s something I’ve heard elsewhere as well. I don’t see any daylight between all-at-once models (advocated by both Adlam and myself) and retrocausal models. But I take causation to be something that can make sense in an all-at-once perspective, because I’m following Judea Pearl and similar interventionist-causation viewpoints. If someone had a different view of causation, I think I can almost see how they would look different.


Maybe it’s worth talking about a case that doesn’t have any time it in at all, like the normal modes of a laser cavity. Those are certainly calculated “all at once”, given the position of the end mirrors. But there’s also a causal story, too: the external intervention points are the end mirror positions, so those are the causes (Pearl’s exogenous variables). The allowed normal modes in the middle are the effect (being correlated with the causes, but not under direct control). There’s a continuous spatial path from the end mirrors to every point in the middle, so it makes sense to talk about the causation “going” from the ends to the middle (in a causal-modelling sense, not in a temporal sense). That’s the sort of causation we’re talking about in the V- and W- geometries; it’s solved all-at-once, but even so, the causal pathways can still be identified. And, the interactions are locally mediated. There’s no leap from one side to the other; there are local mediators in the middle. (That’s a detail that’s far more important to me than to Adlam, as it happens.)

Is this compatible with what you mean by "real" retrocausation? I'm not sure what you mean by that.


In my view, with everything mediated by events in spacetime, neither retrocausal nor all-at-once models are compatible with a psi-ontic viewpoint. The wavefunction doesn’t fit in spacetime (for more than one particle), so any spacetime-based account has got to be psi-epistemic. But there’s not really any existing interpretation to piggyback upon: you can’t just simply add retrocausation to an existing non-retrocausal model. The closest useful starting point is the “weak value” formalism, which is already technically retrocausal. If you’re interested, you can read about how I think this might work here, in a way that would get the wavefunction out of the ontology, while leaving behind the local weak values: https://arxiv.org/abs/2412.05456 .

 

[Sambuco]

Thanks you for your detailed response! Now I think your proposal is clearer to me.

Thanks for the question! I’d like to understand your perspective better, in part because it’s something I’ve heard elsewhere as well. I don’t see any daylight between all-at-once models (advocated by both Adlam and myself) and retrocausal models. But I take causation to be something that can make sense in an all-at-once perspective, because I’m following Judea Pearl and similar interventionist-causation viewpoints. If someone had a different view of causation, I think I can almost see how they would look different.

Maybe it’s worth talking about a case that doesn’t have any time it in at all, like the normal modes of a laser cavity. Those are certainly calculated “all at once”, given the position of the end mirrors. But there’s also a causal story, too: the external intervention points are the end mirror positions, so those are the causes (Pearl’s exogenous variables). The allowed normal modes in the middle are the effect (being correlated with the causes, but not under direct control). There’s a continuous spatial path from the end mirrors to every point in the middle, so it makes sense to talk about the causation “going” from the ends to the middle (in a causal-modelling sense, not in a temporal sense). That’s the sort of causation we’re talking about in the V- and W- geometries; it’s solved all-at-once, but even so, the causal pathways can still be identified. And, the interactions are locally mediated. There’s no leap from one side to the other; there are local mediators in the middle. (That’s a detail that’s far more important to me than to Adlam, as it happens.)

Is this compatible with what you mean by "real" retrocausation? I'm not sure what you mean by that.

I may be wrong, but I see that in the community of foundations of quantum mechanics, "causation" is often used in a broader sense than that associated with an interventionist perspective. For example, if I turn on a lamp at A, I can illuminate the sheet of paper on the table at B, whereas if I don't turn it on, the room remains dark (counterfactual), from which I conclude that "turning on the light" is the cause, in the sense you describe. However, within the most common interpretation of classical electromagnetism, in addition to the above, it is assumed that there is something "real", the field, that transports the information from A to B. I think this second perspective is more in line with Bell's "local causality", which is strongly linked to the notion of realism. That's more in line with the term "real retrocausation" I was referring to.

I think your proposal includes causation in its first (interventionist) sense, but I'm not sure whether it also includes the second. I think that's the difference you're mentioning between your perspective and Adlam's. Am I right?

But there’s not really any existing interpretation to piggyback upon: you can’t just simply add retrocausation to an existing non-retrocausal model.

I find this very interesting. I don't quite understand why retrocausality (à la Pearl) couldn't be incorporated into a framework such as RQM (perhaps Adlam's RQM+CPL version would be better to avoid everything related to the perspectivalism of Rovelli's original version).

The closest useful starting point is the “weak value” formalism, which is already technically retrocausal. If you’re interested, you can read about how I think this might work here, in a way that would get the wavefunction out of the ontology, while leaving behind the local weak values: https://arxiv.org/abs/2412.05456 .

Thanks for the article, I'll take a look!

Lucas.

 

[Ken Wharton]

(clearly I haven't figured out this 'quote' thing yet...)

However, within the most common interpretation of classical electromagnetism, in addition to the above, it is assumed that there is something "real", the field, that transports the information from A to B. I think this second perspective is more in line with Bell's "local causality", which is strongly linked to the notion of realism. That's more in line with the term "real retrocausation" I was referring to.

Okay, lots to unpack here. First: the ontology itself, the part of it based in spacetime, is what Bell called the "local beables". Yes, in most retrocausal models there is a real ontology, some actual parameters associated with points or regions in spacetime. (For example, the fields in E&M, as you say.). So Retrocausal models are models of local beables. That's sort of a prerequistite for talking about most of this stuff.

Even if a given model has local beables, the model might not have local mediation, or $\lambda$-mediation as some people call it. I am interested in models with local mediation (Adlam isn't so concerned about this.). The idea is if there's a cause at A, and an effect at B, it's reasonable to expect to also see effects stretching from A to B via some path in spacetime. But if you hold the middle region fixed, conditional on it being fixed you can't have any causal influences from one side to the other (unless there's some alternate path). That also happens in classical E&M, and it's the sort of retrocausal model that I'm interested in: models that are "locally mediated", as we put it in the title of our above-cited Rev. Mod. Phys. piece.

But where I'm going to push back is the idea that these beables in the middle are somehow "transporting information" from one place to another. That's not how it works in all-at-once or retrocausal models, and arguably not even how it works in E&M. The beables are there, and they would have been different if the inputs to the model were different, and they can be used to help explain the model outputs. But they shouldn't be viewed as some sort of physical conveyer of information, as if casual influences were dynamical objects. Causation is not a dynamical process that flows from one place to another. It is a set of counterfactual statements about how a model works -- if this were different, but that was the same, then this would happen instead of that. Many people think you can't even talk about causation in terms of a one-actual-universe situation, only in terms of possible universes. (I'm an exception, but getting into that topic is quite 'in the weeds'!)

So: real beables, yes. Real mediators in the middle, yes. Real "transportation of information", no. But that last one isn't causation, just a conflation between our causal and dynamical reasoning. Causal reasoning in retrocausal models is best done "all at once".

I find this very interesting. I don't quite understand why retrocausality (à la Pearl) couldn't be incorporated into a framework such as RQM (perhaps Adlam's RQM+CPL version would be better to avoid everything related to the perspectivalism of Rovelli's original version).

Maybe it can, but I'm highly skeptical. If retrocausal models end up being correct, the whole mathematical framework of QM will be seen as a mashup of actual and possible worlds, awkwardly updated only at the very last instant when a measurement is actually made. If that final measurement setting is important right from the start, at some hidden-variable level, why would we use a framework that was built to explicitly ignore it, without any hidden variables?

Thanks for the questions!

 

[Sambuco]

Thanks again for your detailed response! After reading it and rereading the article in Rev. Mod. Phys., I feel I understand the whole issue much better. Correct me if I'm wrong, but I think you're not trying to "reinterpret" conventional wavefunction-based QM or "reconstruct" the usual formalism, as is the case with the proposals of the so-called "quantum reconstruction program" (Stuckey, Masanes, Hardy, Höhn). Rather, you're trying to develop a new formulation of quantum mechanics, but based solely on entities that "live" in spacetime.

Even if a given model has local beables, the model might not have local mediation, or λ-mediation as some people call it.

Are the parameters associated with $\lambda$ also considered part of the ontology?

The idea is if there's a cause at A, and an effect at B, it's reasonable to expect to also see effects stretching from A to B via some path in spacetime.

But where I'm going to push back is the idea that these beables in the middle are somehow "transporting information" from one place to another. That's not how it works in all-at-once or retrocausal models, and arguably not even how it works in E&M. The beables are there, and they would have been different if the inputs to the model were different, and they can be used to help explain the model outputs. But they shouldn't be viewed as some sort of physical conveyer of information, as if casual influences were dynamical objects.

Isn't there a kind of contradiction between the two paragraphs? I understand it to be something like A and B being causally connected by a path through space-time, but that doesn't mean anything is "traveling" along that path. Is this what you mean?

So: real beables, yes. Real mediators in the middle, yes. Real "transportation of information", no. But that last one isn't causation, just a conflation between our causal and dynamical reasoning.

I'm trying to "digest" this

Maybe it can, but I'm highly skeptical.

After rereading the paper, I agree with this. Interpretations like RQM assume an ontology based solely on "events," without $\lambda$-mediation, so the starting point is entirely different.

I have two brief questions/comments:

1. Considering causality from an interventionist perspective, this might suggest that the model is about how an observer (agent?) interacts with a system. What do you think about this? Similarly, if we assume that these kinds of models are, in some sense, fundamental, how do we address a problem where observers aren't typically considered, such as in cosmology?

2. Regarding signal causality, I'm also trying to understand how the hypothesis that outputs cannot depend on future inputs (retrocausality resides in hidden parameters) doesn't break time symmetry. I'll read Almada's paper (arxiv.1510.03706) to better understand this.

Lucas.

 

[Ken Wharton]

Hi Lucas -- it sounds like you're reading all this pretty carefully. Yes, the aim is much more a "reformulation" than an interpretation. I think the goal should be to explain the quantum phenomena themselves, not the mathematics of QM. And yes, the hidden variables must certainly be part of the ontology. I also think you have the right sense that causation shouldn't be said to "travel". Think about it in terms of a block universe. The parameters are all there, in spacetime; nothing "moves" in the block. And yet a model of those parameters can still exhibit causal effects if you change the inputs. So interventionist causation still makes sense.

Your "brief questions" are really big ones, though...

1. Considering causality from an interventionist perspective, this might suggest that the model is about how an observer (agent?) interacts with a system. What do you think about this? Similarly, if we assume that these kinds of models are, in some sense, fundamental, how do we address a problem where observers aren't typically considered, such as in cosmology?

That’s a pretty in-depth question, and the answers are somewhat handwavy at this stage, but certainly when you zoom out of a localized causal model you get a new causal model, with the new “inputs” on the new boundary. We can’t model an agent, but we can imagine that there *is* a model of an agent which could in principle be included in a big system. And unlike the usual problems with zooming out in conventional quantum theory, here you wouldn’t have a mismatch between “quantum stuff in Hilbert space” and “agents in spacetime”. Everything would be in spacetime, so that would resolve of what I see as the trickiest aspect of the measurement problem.

When you zoom *all* the way out, to some cosmological boundary condition, that condition itself would have to serve as the ultimate “input” to the causal model, but that might be okay, too. Of course none of this can be made precise until we have an ontological model of exactly what sorts of external constraints can be imposed on subsystems from the outside.

2. Regarding signal causality, I'm also trying to understand how the hypothesis that outputs cannot depend on future inputs (retrocausality resides in hidden parameters) doesn't break time symmetry. I'll read Almada's paper (arxiv.1510.03706) to better understand this.

You mean, where does the time-asymmetry come from in ordinary interventionist causation? That’s another very big question, but the short answer is that the sorts of causal models we find useful are those with past inputs, because we take ourselves to be able to directly control past inputs but not future outputs. So the time-asymmetry in our physics models comes from *us*, and our ability to control some things but not others. (The asymmetry doesn’t come from the microscopic laws of physics; that’s all nicely time-symmetric, allowing for the possibility of hidden retrocausation, even given that we can’t signal into the past.) Now, the follow-up question is: what puts an effective time-asymmetry on us agents? And that’s another big topic, but it’s not really a question for quantum physics. Most conventional wisdom says this can also be explained in terms of cosmological boundary conditions, and does not require time-asymmetric microscopic physics.

 

[Sambuco]

Hi Ken. I've tried to read a little more about this whole thing to understand it better, and I think I've succeeded to some extent.

Regarding interventionist-based causality and its relationship to the common use of the cause-effect relationship even when no agents are involved, I borrow the following phrase from a recent article by Renato Renner (arxiv.2505.21797):

"the causal link between the moon and tides is understood because, in principle, altering the moon’s mass or position would affect tidal patterns, even if such interventions are not feasible."

Do you think this is a convenient way to describe the type of causality that would exist in your models?

And unlike the usual problems with zooming out in conventional quantum theory, here you wouldn’t have a mismatch between “quantum stuff in Hilbert space” and “agents in spacetime”. Everything would be in spacetime, so that would resolve of what I see as the trickiest aspect of the measurement problem.

Yes, I realize this is one of the main motivations behind these types of models. I assume you're familiar with Sutherland's time-symmetric formulation of Bohm's theory. Do you think it's similar to the type of models you're looking for?

You mean, where does the time-asymmetry come from in ordinary interventionist causation? That’s another very big question, but the short answer is that the sorts of causal models we find useful are those with past inputs, because we take ourselves to be able to directly control past inputs but not future outputs. So the time-asymmetry in our physics models comes from *us*, and our ability to control some things but not others. (The asymmetry doesn’t come from the microscopic laws of physics; that’s all nicely time-symmetric, allowing for the possibility of hidden retrocausation, even given that we can’t signal into the past.) Now, the follow-up question is: what puts an effective time-asymmetry on us agents? And that’s another big topic, but it’s not really a question for quantum physics. Most conventional wisdom says this can also be explained in terms of cosmological boundary conditions, and does not require time-asymmetric microscopic physics.

Crystal clear!

Lucas.